The 26-year-old has joined on a permanent deal from Blackburn Rovers, and has expressed his delight at sealing a move to the Eagles.
"It's been a long day and a long transfer window with a lot of speculation, so it's nice to finally put pen to paper and get it done. I'm looking forward to the next three-and-a-half years," he told the club's official website.
"Any professional footballer will tell you that they want to be in the Premier League. It's something I've done before and really enjoyed and having the opportunity to come and play here for the next couple of years, do well and help the team - it's something I really wanted to do and I'm glad that it's all gone through."
Dann previously played in the Premier League for Birmingham City.